We discuss a robust image authentication scheme based on a hash string constructed from leading JPEG2000 packet data. Motivated by attacks against the approach, key-dependency is added by means of employing a parameterized lifting scheme in the wavelet decomposition stage. Attacks can be prevented effectively in this manner and the security of the scheme in terms of unicity distance is assumed to be high. Key-dependency however can lead to reduced sensitivity of the scheme. This effect has to be compensated by an increase of the hash length which in turn decreases robustness.